This invention relates to a process for determining the position of a moving object using magnetic gradientmetric measurements.
We will start by describing existing positioning/tracking methods based firstly on the use of electromagnetic measurements.
If the quasi-static signature of the electromagnetic source is used, the useful pass band varies from a few kilohertz to 10xe2x88x925 Hz. Document reference [1] at the end of the description contains an analysis of different means of measuring the electrical and magnetic field within this frequency band.
Vector Measurement Means
The electrical field E and the magnetic field B are intrinsically vector magnitudes. Directional systems capable of measuring each of the three components of the magnitude are frequently used in order to measure all information available in this type of signal.
For electrical measurements, a distinction is made firstly between the measurement of a potential difference between two electrodes. The electrical system must then have a large input impedance so that the measurement is not disturbed as described in document reference [2]. Another technique provides access to the electrical field in a conducting medium through a measurement of the electrical current passing between two electrodes, the contact impedances of the electrodes being perfectly adapted to the ambient medium; this is called the xe2x80x9ccurrent collection methodxe2x80x9d (see document reference [3]).
Vector magnetometers also measure vector components of the magnetic field in the directions of each of the magnetometer axes. For example there are xe2x80x9cFluxgatexe2x80x9d magnetometers that are based on the principle of generating a compensation current to compensate the field to be measured in an iron core characterized by its hysteresis cycle, as described in document reference [4]. Another technique is based on a direct measurement of the magnetic flux in xe2x80x9cFluxmeterxe2x80x9d bars, but this type of instrumentation is not well adapted to the measurement of magnetic fields at low frequencies. Finally, SQUID (xe2x80x9cSuperconducting Quantum Interference Devicexe2x80x9d) magnetometers as described in document reference [5] are some of the most efficient devices since their resolution can be as high as 10xe2x88x926 nT.Hzxe2x88x92xc2xd (the nanoTesla or nT being the most frequently used unit). Their superconducting technology requires an expensive cryogenic module that is difficult to use, and are usually used in gradientmetry due to their high precision; the difference between two nearby measurements is equivalent to a differentiation that automatically eliminates remote noise sources.
Scalar Magnetometers
One serious difficulty with magnetic field measurements is the presence of the earth""s magnetic field that can be considered as constant in time for the scales considered, and that has an amplitude of 45000 nT in France. However it is not always possible to guarantee that there is no movement in the measurement direction, and it is very difficult to compensate for these displacements when they induce variations of the field with time within the useful frequency band. For example, a movement of 1 degree in a 45000 nT field generates 100 times more noise than the noise level of sensors in the zero to one Hertz band.
Scalar magnetometers overcome this difficulty by measuring the modulus of a total magnetic field, in other words the modulus of the vector sum of the earth""s magnetic field (about 45000 nT in France) and the vector disturbance considered (a few nT). Nuclear magnetic resonance probes thus measure the precession frequency of protons or electrons (Larmor frequency) that is proportional to the modulus of the ambient field. The resolution can be as high as 10xe2x88x923 nT.Hzxe2x88x92xc2xd.
Given the relative disproportion between the modulus of the earth""s field and the value of the disturbance due to the presence of the object, a good approximation as described in document reference [6] consists of assuming that the sensors measure the modulus of the earth""s field plus the projection of the disturbance onto the earth field vector, as shown in FIG. 1. FIG. 1 illustrates the comparison between the vector sum of the earth""s magnetic field Bt and the measured magnetostatic disturbance Bsignal, and the algebraic sum of the earth""s magnetic field and the projection of the disturbance onto the earth""s magnetic field vector. Scalar magnetometers measure Btotal and not Bsignal. Assuming that a high pass filter was sued to eliminate the DC component and therefore the modulus of the earth""s field, the scalar magnetic measurement is then written:
Bscal=Bsignalxe2x88x92Ut
One of the advantages of these devices, apart from the precisions achieved, is that there is no measurement direction, which makes them easier to use; probes may be placed in any mobile system, and are generally easier to deploy than vector systems.
However, document reference [7] emphasizes the degenerescence of the projection of an essentially vector magnitude (the disturbance) onto a constant vector (the earth""s field). Therefore, this type of magnetometer is conventionally used in detection, but this type of sensor has never yet been used for positioning of sources from a single observation site.
Gradientmetric Devices for Measuring the Magnetic Field
Vector or scalar magnetic devices are used to make two types of measurements, firstly the field which is the basic technique since sensors usually provide uniform magnitudes in the magnetic field, and secondly the spatial gradient of the field.
For SQUID magnetometers, the gradient measurement consists of taking the difference between two spatially close measurements, which is intrinsically equivalent to a differentiation.
In practice, this technique eliminates the contribution of far sources that are usually sources of noise (earth""s magnetic fields, geomagnetic noise, etc.). Thus, although equations for the decay in the amplitude of signals are degraded due to the differentiation (1/r4 instead of 1/r3 for field measurements), the best reduction of disturbing noises can result in equivalent ranges (for example SQUIDs).
Note also that some positioning techniques are intrinsically based on gradient measurements, for example magneto-encephalography (MEG) techniques. This is also the case of this invention, and of the technique most resembling it discussed throughout the rest of this document.
One difficulty lies in adjusting the base length of the gradientmeter; this length can be fixed by carrying out a parametric study based on COR (Curves of the Operating Receptor) detection curves, that are a conventional tool according to detection theory, while respecting the assumption of a differential measurement; therefore, it is checked that the sensor spacing remains small compared with the distance from the source.
This latter constraint makes it possible to intrinsically talk about a xe2x80x9csingle observation sitexe2x80x9d, even when several sensors are used to make the gradientmeters. In this case, it is assumed that the overall gradientmetric measurement device forms a single measurement site.
We will now consider magnetostatic positioning/tracking techniques using a single observation site.
Magnetostatic indiscretion of a ship or a vehicle is due to the ferromagnetic properties of the materials from which it is made, including the steel structure, metal plates, engines, propeller shafts, etc. This object type is modeled with good precision by a single magnetic dipole, as soon as the distance from the measurement system is a few times more than the largest dimension of the object.
The magnetic moment M of this object is then broken down into two parts:
A permanent magnetization that reflects the magnetic history of the object; it is a constant magnetization within a coordinate system related to the object, regardless of the direction of the ambient magnetic field.
An induced magnetization that is due to the magnetic susceptibility of the ferromagnetic materials. In the presence of an external magnetic excitation (in this case the earth""s magnetic field) the elementary ferromagnetic dipoles are oriented along a common direction and produce a non-zero resultant.
In the case of a uniform movement along a straight line, the orientation of the object is constant within the earth""s magnetic field, the spatial variability of which is negligible at the scales considered; therefore, the induced part of the magnetic moment does not vary with time or in space. Within the framework of this assumption about the displacement of the source, the total moment M of magnetic object is assumed to be constant in time and space.
The magnetostatic field of a ferromagnetic object appears as a disturbance in the earth""s magnetic field. This disturbance is a vector disturbance and is written:   B  =                                          μ            0                    ⁢          3          ⁢                      u            .                          u              T                                      -        I                    4        ⁢        π        ⁢                  xe2x80x83                ⁢                  r          3                      ⁢    M  
where rxe2x80x2 denotes the vector of the relative position of the source with respect to the magnetometer, r denotes the modulus of rxe2x80x2, u represents the elementary vector in this direction (u=rxe2x80x2/r) and I is the 3xc3x973 identity matrix. Note that this expression is strongly non-linear for geometric parameters, although it is linear with respect to the magnetic moment.
In a conventional Cartesian coordinate system, this expression becomes:                                           [                                                                                B                    x                                                                                                                    B                    y                                                                                                                    B                    z                                                                        ]                    =                                                                      μ                  0                                                  4                  ⁢                                      xe2x80x83                                    ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                                      π                    5                                                              ⁡                              [                                                                                                                              3                          ⁢                                                      xe2x80x83                                                    ⁢                          Δ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      x                            2                                                                          -                                                  r                          2                                                                                                                                    3                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        x                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        y                                                                                                            3                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        x                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        z                                                                                                                                                3                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        y                        ⁢                                                  xe2x80x83                                                ⁢                        Δx                                                                                                                                      3                          ⁢                                                      xe2x80x83                                                    ⁢                          Δ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      y                            2                                                                          -                                                  r                          2                                                                                                                                    3                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        y                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        z                                                                                                                                                3                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        z                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        x                                                                                                            3                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        z                        ⁢                                                  xe2x80x83                                                ⁢                        Δy                                                                                                                                      3                          ⁢                                                      xe2x80x83                                                    ⁢                          Δ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      z                            2                                                                          -                                                  r                          2                                                                                                                    ]                                      ⁡                          [                                                                                          m                      x                                                                                                                                  m                      y                                                                                                                                  m                      z                                                                                  ]                                      ⁢                  
                ⁢                  where          ⁢                      xe2x80x83                    ⁢                      {                                                                                                      Δ                      ⁢                                              xe2x80x83                                            ⁢                      x                                        =                                          x                      -                                              x                        c                                                                                                                                                              r                    =                                                                                            Δ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      x                            2                                                                          +                                                  Δ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      y                            2                                                                          +                                                  Δ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      z                            2                                                                                                                                                                                                      (        3        )            
where x, y and z represent the coordinates of the source, xc, yc and zc the coordinates of the sensor, r the polar distance from the source to the sensor and mx, my and mz represent each of the components of the magnetic moment of the source in the cartesian coordinate system.
As mentioned above, devices are available that provide access to magnetic field gradients, in other words its spatial derivative in a given direction. Therefore in a given three-dimensional coordinate system, the expression of the magnetic field gradients is a tensor with 9 components, some of which are inter-related. Maxwell""s magnetostatic laws stipulate that the divergence of the magnetic field, in other words the plot of the gradients tensor, is zero and that its rotation is also zero, in other words the tensor is symmetric. Therefore the tensor of Gij is composed of the total of five independent terms. This tensor can be written as follows in a cartesian coordinate system:                     G        =                  [                                                                                          ∂                                          B                      x                                                                            ∂                    x                                                                                                                    ∂                                          B                      x                                                                            ∂                    Y                                                                                                                    ∂                                          B                      x                                                                            ∂                    Z                                                                                                                        G                  12                                                                                                  ∂                                          B                      y                                                                            ∂                    y                                                                                                                    ∂                                          B                      y                                                                            ∂                    z                                                                                                                        G                  13                                                                                                  G                    23                                    -                                      G                    11                                    -                                      G                    22                                                                                                xe2x80x83                                                              ]                                    (        4        )            
As shown in equation (3), a fixed magnetic dipole leads to a problem with six constant parameters, or nine constant parameters if the dipole is moving uniformly along a straight line (the same parameters vector plus the three speed parameters), and with six parameters variable as a function of time in the case of an arbitrary trajectory (x, y, z, mx, my, mz)
Use of Vector Magnitudes
One approach suggested in document reference [5] consists of solving the direct problem by using the complete vector gradient tensor that provides nine measurements. Only five of the nine components are really independent and therefore an additional measurement of the total field is necessary to make the problem of positioning fixed objects observable at all times. This method makes no assumptions about the source displacement and calculates the six parameters characteristic of the problem in each iteration. The authors note that it is very sensitive to measurement noise.
Diagonalization of the gradient tensor makes the solution easier. This then gives the true solution and three phantom solutions. If the source is moving, the phantom solutions may be eliminated due to their time behavior. The speed of the source can also be obtained.
In document reference [8], the author proposes a system based on two vector field measurements made on two separate measurement sites. In this application, the objective is to position an alternating dipole with known frequency and moment to study the displacement of dike elements exposed to swell. Since the modulus of the moment is known, the five parameters that are variable in time have to be estimated at each instant. The problem can be inverted if six independent measurements are taken.
In conclusion, it may be emphasized that the large number of components measured using vector measurement systems makes it possible to consider the direct problem without making any assumptions about the movement of the source. However in this case, the large number of unknowns requires the use of several observation sites. The only way of obtaining a complex system that can be treated as a single observation site is the approach using the complete gradient tensor. However as already mentioned, vector devices introduce the difficult problem of positioning measurement axes.
Use of Scalar Magnitudes
Some authors have studied positioning/tracking possibilities without making any assumption about the source movement by using several scalar magnetometers in different geographic locations. In all cases, the authors had difficulties with bad conditioning of the problem and therefore tests were carried out with initializations close to the true values, since there are very many local minima.
Another approach consists of reducing the number of unknowns and using assumptions about displacement of the source whenever possible. One frequently encountered assumption is a uniform movement along a straight line. This assumption is perfectly justifiable in a submarine context since the sources move along headings, and it may also be suitable for other applications such as motorway applications.
Document reference [6] presents a complete study of the signature measured by a directional sensor in the case of this type of relative displacement. It thus shows that the signals are broken down based on orthogonal signals, called Anderson base signals that depend on two parameters, firstly the distance between the sensor and the CPA (Closest Point of Approach) divided by the speed of the source, and secondly the distance from the source to the CPA divided by the speed:                     {                              D            V                    ,                                                    x                -                                  x                  0                                            V                        =                          E              V                                      }                            (        5        )            
This decomposition is valid regardless of the measurement direction, and therefore particularly in the direction of the earth""s magnetic field for scalar type sensors.
Document reference [6] then presents the adapted multi-dimensional filtering technique which is a tool useful for detection/optimum estimating in white noise, making use of a Neyman-Pearson type quadratic criterion.
In practice, this tool requires an appropriate algorithm and high calculation capacities if it is to work in real time. A genuinely operational implementation is described, and parametric studies such as COR detection curves, are described in document reference [7]. The author also proposes a sub-optimal positioning method based on measurements of three observation sites in the case in which the trajectory is located within the plane of the sensors. In this assumption, a single observation site does not give any positioning information since the parameters in equation (5) result in a double ambiguity, both in azimuth and in distance, and two observation sites lead to two or four phantom solutions depending on which algorithm is used to process the magnetic signatures.
Document reference [9] considers the airborne magnetic tracking; the aircraft flies at a constant speed and heading and the submarine source is considered as being motionless, considering the difference in speed between the observer and the observed body. In this case, the sensors are moving uniformly along a straight line with respect to the source, but this subject corresponds to a problem similar to the problem being considered and is quite transposable to it. Scalar sensors are installed at the end of the wing and the author uses differential measurements either between the two magnetometers at the same instant, or between two successive measurements provided by the same sensor. The positioning technique only uses a small number of successive measurements, and the method is then iterated with new measurements. This provides assurance that the source speed is negligible compared with the aircraft speed, but it is only possible to work with high signal-to-noise ratios. Another limitation to this method is due to the orders of magnitudes indicated by the mockup described in the article: the author assumes that the aircraft is flying very close to the water and that its wing span is of the same order of magnitude as the depth of the source. Consequently, the measurements made are not of the gradientmetric type and are more similar to N geographically distributed measurements.
Airborne techniques currently in use consider mainly detection and positioning methods that are based on at least two passes above the source, which is actually similar to observing from two distinct sites.
Documents reference [10] and [11] provide information about the use of very low frequency electromagnetic signatures, for example output from ship corrosion currents.
The first of these documents demonstrates the existence of this type of signature by a campaign of experiments. If the source is moving uniformly along a straight line, the author proposes that the envelope of the signature can be used and demonstrates the existence of an Anderson base of the same type as that described in document reference [6] in the case of magnetostatic signals. Estimated parameters are then of the same type and cannot be used to position the source from a single measurement site.
The second document proposes an inversion of the problem of positioning a fixed electrical dipole, but this technique uses two distinct measurement sites each providing access to the three components of the electrical field.
The presentation of the invention is restricted to the case of a magnetostatic dipole. However, as in document reference [10], an expression equivalent to equation (2) may be used for the quasi-static envelope of very low frequency magnetic signals due to corrosion currents. In the same way as for magnetostatic signals, these signatures may be measured by scalar magnetometers provided that it is possible as a function of their pass band.
The purpose of the invention is an information processing system capable of tracking a source moving uniformly along a straight line from a single observation site, using a type of sensor that does not a priori provide enough information for determining the position from a single observation site, and which is different from devices according to prior art by its ease of use and its compatibility with onboard applications.
The invention relates to a process for determining the position of a moving object characterized in that it comprises the following steps:
scalar measurements are acquired by a set of electromagnetic sensors all installed on the same site, at a position known at each instant;
the trajectory of the object is determined approximately by a model;
the measurements output from each sensor are combined to obtain spatial gradient measurements representative of the vector electromagnetic disturbance of the moving object;
a vector of parameters characteristic of the model is estimated as a function of gradient measurements and as a function of the position of the sensors;
the position of the object is determined as a function of the position of the sensors and the parameters vector.
Advantageously, the following variants are possible:
in a first variant, on which others depend, electromagnetic measurements output from scalar magnetometers used in gradientmeters are used;
in a second variant, the movement of the object is modeled by a uniform movement along a straight line, the parameters vector being (xcex8, 3/v, vxe2x80x2/v), where xcex8 is the azimuth of the object at a reference instant taken with respect to the North, r is the source/sensor distance at the same reference instant, vxe2x80x2 is the speed of the object and v is the modulus of the speed; there is one phantom solution of the genuine solution that is (xcex8+xcfx80, r/v, vxe2x80x2/v);
in a third variant, the number of degrees of freedom in the tracking problem is reduced, for example when a set of possible trajectories of object is known;
in a fourth variant, magnetic measurements are combined with acoustic measurements in order to reduce the set of solutions; by adding measurement equations derived from acoustic information to measurement equations derived from electromagnetic information;
in a fifth variant (a refinement of the third variant), the azimuth method and the Doppler phenomenon observed in the case of sources radiating a narrow band signal around a stable central frequency, are used together;
in a sixth variant, the measurement acquisition device is maneuvered, for example by rotating it or displacing it along its own axis or otherwise, to obtain electromagnetic measurements at another location or from another angle, so that the set of solutions can be reduced by diversifying the set of observation points.
The invention can overcome the use of vector systems for the magnetic measurement. Instead, a technique is used that is based on scalar field measurements. These sensors do not have a preferred measurement direction, which makes the magnetic measurement independent of the orientation of the device. In some applications, this constraint is indispensable (marine applications, moving sensors) and in all other cases, it means that devices can be moved much more simply and quickly.
The invention uses a single observation site, despite the loss of information due to the use of scalar magnetometers to measure vector magnitudes.
In the invention, these scalar sensors are laid out as a gradientmeter within a space that is small compared with the dimensions of the application. In order to avoid re-introducing a measurement direction into the device, it is proposed to use an algorithm that only requires knowledge of the position of the sensors. In doing this, no other restrictive assumption about the variation of the gradientmetric system is necessary (rigid, fixed system, or strictly uniform movement along a straight line). This is particularly useful when the sensors are placed in moving systems, for example at the end of an aircraft wing, as a xe2x80x9cbirdxe2x80x9d, xe2x80x9cfish sonarxe2x80x9d, or buoys, etc.
This type of scalar measurement may be made from three vector magnetometers fixed together.
Faced with the complexity of the positioning problem, vector systems initially appeared unavoidable, particularly when working from a single observation site. The invention overcomes this difficulty by making an assumption about the displacement of the source, so that the problem can be reconditioned.
Although the invention does not guarantee complete observability of the phenomenon, it can be used to estimate a remarkable parameter for a monosite device, namely the azimuth of the source at a given instant.
The only positioning ambiguity is in the parameter denoted r/V. The invention includes a number of variants in which knowledge of this parameter can easily be introduced and which then gives almost complete observability (there may be a phantom solution depending on the application) or complete observability in three dimensions in the best cases with maneuvering.
As described above, different variants are possible; restriction of the number of degrees of freedom of a problem, merging with other indiscretions, for example narrow band acoustic merging, displacement of the carrier with at least one maneuver to make the problem observable.
The process according to the invention can be used to combine several measurement types derived from different physical phenomena such as acoustic phenomena (mentioned above), wide band phenomena, electromagnetic phenomena generated by the loopback of corrosion currents by the sea or emission from the onboard network.
Thus, wide band scalar magnetometers and possibly electrometers are available to make use of the wide band physical phenomenon associated with the electromagnetic emission from a source (ship) due to corrosion currents modulated by the propulsion system. The theory of this phenomenon is described in detail in document reference [10]. Measurements are processed in the same way as before; making use of the components of the electrical dipole moment of the source (assumed with a good approximation to be horizontal, namely one component) and the modulation frequency f0 that can be estimated using a high resolution spectral analysis algorithm.
Other electromagnetic phenomena may be used in marine environments like the electromagnetic emission generated by the loopback of corrosion currents by the sea or emission from the ship""s electrical network. They can be used in the proposed system, all that is necessary is to clearly state the corresponding observability problem and to integrate the corresponding additional parameters into the measurement and state vectors.